Advanced Inertial Sensors, Navigation, and Fusion

This paper presents a sensor fusion method for navigation of unmanned underwater vehicles. The method combines Lie theory into Kalman filter to estimate and compensate for the misalignment between the sensors: inertial navigation system and Doppler Velocity Log (DVL). In the process and measurement model equations, a 3-dimensional Euclidean group ($\mathit{SE}\left(3\right)$) and 3-sphere space (${\mathit{S}}^3$) are used to express the pose (position and attitude) and misalignment, respectively. $\mathit{SE}\left(3\right)$ contains position and attitude transformation matrices, and ${\mathit{S}}^3$ comprises unit quaternions. The increments in pose and misalignment are represented in the Lie algebra, which is a linear space. The use of Lie algebra facilitates the application of an extended Kalman filter (EKF). The previous EKF approach without Lie theory is based on the assumption that a non-differentiable space can be approximated as a differentiable space when the increments are sufficiently small. On the contrary, the proposed Lie theory approach enables exact differentiation in a differentiable space, thus enhances the accuracy of the navigation. Furthermore, the convergence and stability of the internal parameters, such as the Kalman gain and measurement innovation, are improved. Full article

The performance of a hemispherical resonant gyroscope (HRG) is directly affected by the sphericity error of the thin-walled spherical shell of the hemispherical shell resonator (HSR). In the production process of the HSRs, high-speed, high-accuracy, and high-robustness requirements are necessary for evaluating sphericity errors. We designed a sphericity error evaluation method based on the minimum zone criterion with an adaptive number of subpopulations. The method utilizes the global optimal solution and the subpopulations’ optimal solution to guide the search, initializes the subpopulations through clustering, and dynamically eliminates inferior subpopulations. Simulation experiments demonstrate that the algorithm exhibits excellent evaluation accuracy when processing simulation datasets with different sphericity errors, radii, and numbers of sampling points. The uncertainty of the results reached the order of 10⁻⁹ mm. When processing up to 6000 simulation datasets, the algorithm’s solution deviation from the ideal sphericity error remained around −3 × 10⁻⁹ mm. And the sphericity error evaluation was completed within 1 s on average. Additionally, comparison experiments further confirmed the evaluation accuracy of the algorithm. In the HSR sample measurement experiments, our algorithm improved the sphericity error assessment accuracy of the HSR’s inner and outer contour sampling datasets by 17% and 4%, compared with the results given by the coordinate measuring machine. The experiment results demonstrated that the algorithm meets the requirements of sphericity error assessment in the manufacturing process of the HSRs and has the potential to be widely used in the future. Full article

This article explores the implementation of high-accuracy GPS-denied ad hoc localization. Little research exists on ad hoc ultra-wideband-enabled localization systems with mobile and stationary nodes. This work aims to demonstrate the localization of bicycle-modeled robots in a non-static environment through a mesh network of mobile, stationary robots, and ultra-wideband sensors. The non-static environment adds a layer of complexity when actors can enter and exit the node’s field of view. The method starts with an initial localization step where each unmanned ground vehicle (UGV) uses the surrounding, available anchors to derive an initial local or, if possible, global position estimate. The initial localization uses a simplified implementation of the iterative multi-iteration ad hoc localization system (AHLos). This estimate was refined using an unscented Kalman filter (UKF) following a constant turn rate and velocity magnitude model (CTRV). The UKF then fuses the robot’s odometry and the range measurements from the Decawave ultra-wideband receivers stationed on the network nodes. Through this position estimation stage, the robot broadcasts its estimated position to its neighbors to help the others further improve their localization estimates and localize themselves. This wave-like cycle of nodes helping to localize each other allows the network to act as a mobile ad hoc localization network. Full article

In this paper, we explore several widely available software-defined radio (SDR) platforms that could be used for locating with the signal Doppler frequency (SDF) method. In the SDF, location error is closely related to the accuracy of determining the Doppler frequency shift. Therefore, ensuring high frequency stability of the SDR, which is utilized in the location sensor, plays a crucial role. So, we define three device classes based on the measured frequency stability of selected SDRs without and with an external rubidium clock. We estimate the localization accuracy for these classes for two scenarios, i.e., short- and long-range. Using an external frequency standard reduces the location error from 20 km to 30 m or 15 km to 2 m for long- and short-range scenarios, respectively. The obtained simulation results allowed us to choose an SDR with appropriate stability. The studies showed that using an external frequency standard is necessary for minimizing SDR frequency instability in the Doppler effect-based location sensor. Additionally, we review small-size frequency oscillators. For further research, we propose two location sensor systems with small size and weight, low power consumption, and appropriate frequency stability. In our opinion, the SDF location sensor should be based on the bladeRF 2.0 micro xA4 or USRP B200mini-i SDR platform, both with the chip-scale atomic clock CSAC SA.45s, which will allow for minor positioning errors in the radio emitters. Full article

High-accuracy heading angle is significant for estimating autonomous vehicle attitude. By integrating GNSS (Global Navigation Satellite System) dual antennas, INS (Inertial Navigation System), and a barometer, a GNSS/INS/Barometer fusion method is proposed to improve vehicle heading angle accuracy. An adaptive Kalman filter (AKF) is designed to fuse the INS error and the GNSS measurement. A random sample consensus (RANSAC) method is proposed to improve the initial heading angle accuracy applied to the INS update. The GNSS heading angle obtained by a dual-antenna orientation algorithm is additionally augmented to the measurement variable. Furthermore, the kinematic constraint of zero velocity in the lateral and vertical directions of vehicle movement is used to enhance the accuracy of the measurement model. The heading errors in the open and occluded environment are 0.5418° (RMS) and 0.636° (RMS), which represent reductions of 37.62% and 47.37% compared to the extended Kalman filter (EKF) method, respectively. The experimental results demonstrate that the proposed method effectively improves the vehicle heading angle accuracy. Full article

SLAM (simultaneous localization and mapping) plays a crucial role in autonomous robot navigation. A challenging aspect of visual SLAM systems is determining the 3D camera orientation of the motion trajectory. In this paper, we introduce an end-to-end network structure, InertialNet, which establishes the correlation between the image sequence and the IMU signals. Our network model is built upon inertial measurement learning and is employed to predict the camera’s general motion pose. By incorporating an optical flow substructure, InertialNet is independent of the appearance of training sets and can be adapted to new environments. It maintains stable predictions even in the presence of image blur, changes in illumination, and low-texture scenes. In our experiments, we evaluated InertialNet on the public EuRoC dataset and our dataset, demonstrating its feasibility with faster training convergence and fewer model parameters for inertial measurement prediction. Full article

In professional use cases like police or fire brigade missions, coordinated and systematic force management is crucial for achieving operational success during intervention by the emergency personnel. A real-time situation picture enhances the coordination of the team. This situation picture includes not only an overview of the environment but also the positions, i.e., localization, of the emergency forces. The overview of the environment can be obtained either from known situation pictures like floorplans or by scanning the environment with the aid of visual sensors. The self-localization problem can be solved outdoors using the Global Navigation Satellite System (GNSS), but it is not fully solved indoors, where the GNSS signal might not be received or might be degraded. In this paper, we propose a novel combination of an inertial localization technique based on simultaneous localization and mapping (SLAM) with 3D building scans, which are used as prior information, for geo-referencing the positions, obtaining a situation picture, and finally visualizing the results with an appropriate visualization tool. We developed a new method for converting point clouds into a hexagonal prism map specifically designed for our SLAM algorithm. With this combination, we could keep the equipment for first responders as lightweight as required. We showed that the positioning led to an average accuracy of less than 1m indoors, and the final visualization including the building layout obtained by the 3D building reconstruction will be advantageous for coordinating first responder operations. Full article

The article deals with sensor fusion and real-time calibration in a homogeneous inertial sensor array. The proposed method allows for both estimating the sensors’ calibration constants (i.e., gain and bias) in real-time and automatically suppressing degraded sensors while keeping the overall precision of the estimation. The weight of the sensor is adaptively adjusted according to the RMSE concerning the weighted average of all sensors. The estimated angular velocity was compared with a reference (ground truth) value obtained using a tactical-grade fiber-optic gyroscope. We have experimented with low-cost MEMS gyroscopes, but the proposed method can be applied to basically any sensor array. Full article

The Internet of Things (IoT) for smart industry requires the surveillance and management of people and objects. The ultra-wideband positioning system is an attractive solution for achieving centimeter-level accuracy in target location. While many studies have focused on improving the accuracy of the anchor coverage range, it is important to note that in practical applications, positioning areas are often limited and obstructed by furniture, shelves, pillars, or walls, which can restrict the placement of anchors. Furthermore, some positioning regions are located beyond anchor coverage, and a single group with few anchors may not be able to cover all rooms and aisles on a floor due to non-line-of-sight errors causing severe positioning errors. In this work, we propose a dynamic-reference anchor time difference of arrival (TDOA) compensation algorithm to enhance accuracy beyond anchor coverage by eliminating local minima of the TDOA loss function near anchors. We designed a multidimensional and multigroup TDOA positioning system with the aim of broadening the coverage of indoor positioning and accommodating complex indoor environments. By employing an address-filter technique and group-switching process, tags can seamlessly move between groups with a high positioning rate, low latency, and high accuracy. We deployed the system in a medical center to locate and manage researchers with infectious medical waste, demonstrating its usefulness for practical healthcare institutions. Our proposed positioning system can thus facilitate precise and wide-range indoor and outdoor wireless localization. Full article

This paper presents a new type of three-axis gyroscope. The gyroscope comprises two independent parts, which are nested to further reduce the structure volume. The capacitive drive was adopted. The motion equation, capacitance design, and spring design of a three-axis gyroscope were introduced, and the corresponding formulas were derived. Furthermore, the X/Y driving frequency of the gyroscope was 5954.8 Hz, the Y-axis detection frequency was 5774.5 Hz, and the X-axis detection frequency was 6030.5 Hz, as determined by the finite element simulation method. The Z-axis driving frequency was 10,728 Hz, and the Z-axis sensing frequency was 10,725 Hz. The MEMS gyroscope’s Z-axis driving mode and the sensing mode’s frequency were slightly mismatched, so the gyroscope demonstrated a larger bandwidth and higher Z-axis mechanical sensitivity. In addition, the structure also has good Z-axis impact resistance. The transient impact simulation of the gyroscope structure showed that the maximum stress of the sensitive structure under the impact of 10,000 g@5 ms was 300.18 Mpa. The gyroscope was produced by etching silicon wafers in DRIE mode to obtain a high aspect ratio structure, tightly connected to the glass substrate by silicon/glass anode bonding technology. Full article

Navigation and positioning of autonomous underwater vehicles (AUVs) in the complex and changeable marine environment are crucial and challenging. For the positioning of AUVs, the integrated navigation of the strap-down inertial navigation system (SINS), Doppler velocity log (DVL), and pressure sensor (PS) has a common application. Nevertheless, in the complex underwater environment, the DVL performance is affected by the current and complex terrain environments. The outliers in sensor observations also have a substantial adverse effect on the AUV positioning accuracy. To address these issues, in this paper, a novel tightly integrated navigation model of the SINS, DVL, and PS is established. In contrast to the traditional SINS, DVL, and PS tightly integrated navigation methods, the proposed method in this paper is based on the velocity variation of the DVL beam by applying the DVL bottom-track and water-track models. Furthermore, a new robust interacting multiple models (RIMM) information fusion algorithm is proposed. In this algorithm, DVL beam anomaly is detected, and the Markov transfer probability matrix is accordingly updated to enable quick model matching. By simulating the motion of the AUV in a complex underwater environment, we also compare the performance of the traditional loosely integrated navigation (TLIN) model, the tightly integrated navigation (TTIN) model, and the IMM algorithm. The simulation results show that because of the PS, the velocity and height in the up-change amplitude of the four algorithms are small. Compared with the TLIN algorithm in terms of maximum deviation of latitude and longitude, the RIMM algorithm also improves the accuracy by 39.1243 m and 26.4364 m, respectively. Furthermore, compared with the TTIN algorithm, the RIMM algorithm improves latitude and longitude accuracy by 1.8913 m and 11.8274 m, respectively. A comparison with IMM also shows that RIMM improves the accuracy of latitude and longitude by 1.1506 m and 7.2301 m, respectively. The results confirm that the proposed algorithm suppresses the observed noise and outliers of DVL and further achieves quick conversion between different DVL models while making full use of the effective information of the DVL beams. The proposed method also improves the navigation accuracy of AUVs in complex underwater environments. Full article

Pedestrian dead reckoning (PDR) using inertial sensors has paved the way for developing several approaches to step length estimation. In particular, emerging step length estimation models are readily available to be utilized on smartphones, yet they are seldom formulated considering the kinematics of the human body during walking in combination with measured step lengths. We present a new step length estimation model based on the acceleration magnitude and step frequency inputs herein. Spatial positions of anatomical landmarks on the human body during walking, tracked by an optical measurement system, were utilized in the derivation process. We evaluated the performance of the proposed model using our publicly available dataset that includes measurements collected for two types of walking modes, i.e., walking on a treadmill and rectangular-shaped test polygon. The proposed model achieved an overall mean absolute error (MAE) of 5.64 cm on the treadmill and an overall mean walked distance error of 4.55% on the test polygon, outperforming all the models selected for the comparison. The proposed model was also least affected by walking speed and is unaffected by smartphone orientation. Due to its promising results and favorable characteristics, it could present an appealing alternative for step length estimation in PDR-based approaches. Full article

In order to improve the initialization robustness of visual inertial SLAM, the complementarity of the optical flow method and the feature-based method can be used in vision data processing. The parallel initialization method is proposed, where the optical flow inertial initialization and the monocular feature-based initialization are carried out at the same time. After the initializations, the state estimation results are jointly optimized by bundle adjustment. The proposed method retains more mapping information, and correspondingly is more adaptable to the initialization scene. It is found that the initialization map constructed by the proposed method features a comparable accuracy to the one constructed by ORB-SLAM3 in monocular inertial mode. Since the online extrinsic parameter estimation can be realized by the proposed method, it is considered better than ORB-SLAM3 in the aspect of portability. By the experiments performed on the benchmark dataset EuRoC, the effectiveness and robustness of the proposed method are validated. Full article

In response to the lack of specific demonstration and analysis of the research on the necessity of the Lie group strapdown inertial integrated navigation error model based on the Euler angle, two common integrated navigation systems, strapdown inertial navigation system/global navigation satellite system (SINS/GNSS) and strapdown inertial navigation system/doppler velocity log (SINS/DVL), are used as subjects, and the piecewise constant system (PWCS) matrix, based on the Lie group error model, is established. From three aspects of variance estimation, the observability and performance of the system with large misalignment angles for low, medium, and high accuracy levels, traditional error model, Lie group left error model, and right error model are compared. The necessity of research on Lie group error model is analyzed quantitatively and qualitatively. The experimental results show that Lie group error model has better stability of variance estimation, estimation accuracy, and observability than traditional error model, as well as higher practical value. Full article